Use the Following Results the Polar Equation of the Hyperbolla $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$

question 45

Multiple Choice

Use the following results the polar equation of the hyperbolla $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is $r ^ { 2 } = \frac { - b ^ { 2 } } { 1 - e ^ { 2 } \cos ^ { 2 } \theta }$ to write the polar form of the equation of the conic $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ . ​

• A) \(r ^ { 2 } = \frac { 144 } { 16 \cos ^ { 2 } \theta + 25 }\)
• B) \(r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta - 16 }\)
• C) \(r ^ { 2 } = \frac { 144 } { 25 \cos ^ { 2 } \theta + 16 }\)
• D) \(r ^ { 2 } = \frac { - 144 } { 25 \cos ^ { 2 } \theta + 16 }\)
• E) \(r ^ { 2 } = \frac { 144 } { 16 - 25 \cos ^ { 2 } \theta }\)

---

Definitions:

Investment

The allocation of resources, such as capital or time, in expectation of future returns, typically in the form of profit, interest, or appreciation in value.

Stocks and Bonds

Financial instruments representing ownership in a company (stocks) and debt obligations issued by entities (bonds), respectively, used for investment purposes.

Private Enterprise

Private enterprise is a business or industry that is managed and owned by private individuals or companies rather than by the state.

Production Possibility Frontier

A diagram demonstrating all possible maximal production outcomes for two commodities, subject to a combination of resources and various factors.